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Of Plane Figures.

Second. The rectangle, which has its angles right angles, and its opposite sides equal and parallel.

Third. The parallelogram, which has its opposite sides equal and parallel, but its angles not right angles.

Fourth. The rhombus, which has all its sides equal, and the opposite sides parallel, without having its angles right angles.

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Fifth. The trapezoid, which has only two of its sides parallel.

15. The base of a figure is the side on which it stands, and the altitude is a line drawn from the top, perpendicular to the base.

16. A diagonal, is a line joining the vertices of two angles not adjacent. Thus, AB is a diagonal.

B

QUEST.-What is a rectangle? What is a parallelogram? What is a rhombus? What is a trapezoid? 15. What is the base of a figure? 16. What is a diagonal?

Of Surfaces.

SECTION V.

OF THE UNIT OF LENGTH, AND THE MEASURE

OF SURFACES.

1. If the length of a line be computed in feet, one foot is the unit of the line, and is called the linear unit.

If the length of a line be computed in yards, one yard is the linear unit. If it be computed in rods, one rod is the linear unit; and if it be computed in chains, one chain is the linear unit.

2. If we describe a square on the unit of length, such square is called the unit of surface. Thus, if the linear unit be 1 foot, one square foot will be the unit of surface.

QUEST.-1. If the length of a line be computed in feet, what is the unit of the line? What is this unit called? If the length of a line be computed in yards, what is the linear unit? If it be computed in rods, what is the linear unit? 2. If a square be described on the unit of length, what is it called? If the unit of length be one foot, what is the unit of surface ?

Of Surfaces.

3. If the linear unit is 1 yard, one square yard will be the unit of surface; and this square yard contains 9 square feet.

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4. If the linear unit is 1 chain, the unit of surface will be 1 square chain, which will contain 16 square rods.

1 chain 4 rods.

5. Lands are generally estimated in acres, roods, and perches or square rods.

1 Acre 4 roods=160 Perches or square rods.

1 Rood 40 perches

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of an Acre.

6. If we have a rectangle whose base is 4 feet, and altitude 3 feet, it is evident that it will contain 12 square feet. These 12 square feet are the measure of the surface of the rectangle.

QUEST.-3. If the unit of length be one yard, what is the unit of surface? 4. If the linear unit be one chain, what is the unit of surface? 5. In what are lands generally estimated? How many rocds in an acre? How many perches in an acre? 6. What is the content of a rectangle whose base is 4 feet, and altitude 3 feet? What are these twelve square feet called?

Of Surfaces.

It is plain that the number of squares in any rectangle, will be expressed by the units of its base, multiplied by the units in its altitude. This product is called the measure of the rectangle.

In geometry, we often say, the rectangle of two lines, by which we mean, the rectangle of which those lines are the two adjacent sides.

7. The Area of a figure, is the measure of its surface. It should be remembered that, the unit of the number which expresses the area, is a square of which the linear

unit is the side.

8. The area of a rectangle is equal to the product of its base by its altitude. If the base of a rectangle is 30 yards, and the altitude 5 yards, the area will be 150 square yards.

9. The area of a square is equal to the product of its two equal sides; that is, to the square of one of its sides.

QUEST.-What is the number of squares in any rectangle equal to ? When you speak of the rectangle of two lines, what do you mean? 7. What is the area of a figure? What is the unit of the number which expresses the area? 8. What is the area of a rectangle equal to ? If the base of a rectangle is 10, and altitude 4 feet, what is its area? If the base be 12 yards, and altitude 5 yards, what is its area? If the base be 9 rods, and altitude 8 rods, what is its area? 9. What is the area of a square equal to ? If the side of a square is 3 feet, what is its area? If the side be 9 yards, what is its area? If the side be 8 rods, what is its area?

Of Surfaces.

10. The altitude of a parallelogram is the perpendicular distance between two of its parallel sides. Thus, EB is the altitude of the parallelogram ABCD.

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11. The area of a parallelogram is equal to its base multiplied by its altitude. Thus, the area of the parallelogram ABCD, is equal to AB×BE.

If the base is 20, and altitude 15 feet, the area will be 300 square feet.

12. The area of a trapezoid is equal to half the sum of its parallel sides multiplied by the perpendicular distance between them. Thus,

A

area ABCD=(AB+CD)× CF.

13. The diagonal DB divides the rectangle ABCD into two equal triangles. Hence, a triangle is half a rectangle, having the same base and altitude.

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QUEST.-10. What is the altitude of a parallelogram? 11. What is the area of a parallelogram equal to? If the base of a parallelogram be 10 feet, and the altitude 5 feet, what is the area? 12. To what is the area of a trapezoid equal? If the two parallel sides of a trapezoid are 8 and 10, and the altitude 7, what is the area? 13. How does the diagonal of a rectangle divide it? If a rectangle and a triangle have the same base and altitude, how do they compare with each other?

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